Where does that green wire go in the second picture? Remember, in house wiring, at least in NA, BLACK is HOT! If that green ground wire goes into the wire nut with the black wire from the cord, that would be a dead short to ground. And if the breaker was not tripping, it would also be making the casement live with 120.
When you are saying no reading, is the meter showing 0.00 or Overload? Remember when reading Ohms, 0.00 is not infinite resistance, it is no resistance (lots of current).
Given the load you tested the breaker with I can some what rule out a bad breaker. That is a big air compressor and a head gun is a descent load. So a good test of the breaker. I would advise NOT opening the electric panel for any reason as the currents in there are enough not only you kill some one but leave them crispy.
If I was going to keep troubleshooting this issue I would follow the black wire out of the wire nut and look for any wires that were nicked pinched or frayed also look for black marks anything shorting with THAT much current will most likely cause some charring and smoke damage.
The typical disclaimer you are proceeding at your own risk. Electricity can and will injure or kill. If you do not know what you are doing DO NOT proceed If you THINK you know what you are doing DO NOT proceed.